Question 1

Find the empirical regression line y = a + bx for the data (x , y) = (1, -2), 4, 1), and (1, 10). What is the predicted value of y when x = -3?

Accepted Answer

a = 5 and b = -1; empirical re

Question 2

Find the absolute maximum and minimum values of f(x, y) = y2 - y - x - 5 on the square0 $\le$x $\le$ 1, 0 $\le$y $\le$ 1.

Accepted Answer

A)  maximum 0, minimum -   
B)  maximum -   , minimum -   
C)  maximum -5, minimum -   
D)  maximum -5, minimum -   
E)  maximum -   , minimum -5 
A)  maximum 0, minimum -   
B)  maximum -   , minimum -   
C)  maximum -5, minimum -   
D)  maximum -5, minimum -   
E)  maximum -   , minimum -5

Question 3

Find the maximum and minimum values of f(x, y) = (x - y)   .

Accepted Answer

A)  maximum   , minimum 0 
B)  maximum   , minimum   
C)  maximum     , minimum -     
D)  maximum 2   , minimum 0 
E)  maximum   , minimum -   
A)  maximum   , minimum 0 
B)  maximum   , minimum   
C)  maximum     , minimum -     
D)  maximum 2   , minimum 0 
E)  maximum   , minimum -

Question 4

Find the envelope of the family of straight lines y - 3   x + 2   = 0.

Accepted Answer

A)  y = x3 
B)  y = 2x3 
C)  y2 = x3 
D)  y2 = 3x3 
E)  y = 3x3 
A)  y = x3 
B)  y = 2x3 
C)  y2 = x3 
D)  y2 = 3x3 
E)  y = 3x3

Question 5

Find the values of constant real numbers a and b to minimize   dx.

Accepted Answer

A)  a = 15 , b = -1 
B)  a = 19 , b = -   
C)  a = - 24 , b = 4 
D)  a = -   , b =   
E)  a = 24 , b = - 4 
A)  a = 15 , b = -1 
B)  a = 19 , b = -   
C)  a = - 24 , b = 4 
D)  a = -   , b =   
E)  a = 24 , b = - 4

Question 6

Find the absolute maximum and minimum values of f(x, y) = 2 - x2 - 4y on the diskx2 + y2 $\le$ 9.

Accepted Answer

A)  maximum 16, minimum -14 
B)  maximum 10, minimum -13 
C)  maximum 14, minimum -11 
D)  maximum 12, minimum -10 
E)  none of the above 
A)  maximum 16, minimum -14 
B)  maximum 10, minimum -13 
C)  maximum 14, minimum -11 
D)  maximum 12, minimum -10 
E)  none of the above

Question 7

Find the absolute maximum and minimum values of f(x, y, z) = xyz(1 - x2 - y2 - z2) on the tetrahedron bounded by x = 0, y = 0, z = 0, and x + y + z = 2.

Accepted Answer

A)  maximum   , minimum 0 
B)  maximum   , minimum 0 
C)  maximum   , minimum 0 
D)  maximum   , minimum 0 
E)  none of the above 
A)  maximum   , minimum 0 
B)  maximum   , minimum 0 
C)  maximum   , minimum 0 
D)  maximum   , minimum 0 
E)  none of the above

Find the empirical regression line y = a + bx for the data (x , y) = (1, -2), 4, 1), and (1, 10). What is the predicted value of y when x = -3?

Find the absolute maximum and minimum values of f(x, y) = y² - y - x - 5 on the square0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 1.

Find the maximum and minimum values of f(x, y) = (x - y) .

Find the envelope of the family of straight lines y - 3 x + 2 = 0.

Find the values of constant real numbers a and b to minimize dx.

Find the absolute maximum and minimum values of f(x, y) = 2 - x² - 4y on the diskx² + y² $\le$ 9.

Find the absolute maximum and minimum values of f(x, y, z) = xyz(1 - x² - y² - z²) on the tetrahedron bounded by x = 0, y = 0, z = 0, and x + y + z = 2.

Preliminaries

Limits and Continuity

Differentiation

Transcendental Functions

More Applications of Differentiation

Integration

Techniques of Integration

Applications of Integration

Conics, Parametric Curves, and Polar Curves

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Exam 14: Applications of Partial Derivatives

Find the empirical regression line y = a + bx for the data (x , y) = (1, -2), 4, 1), and (1, 10). What is the predicted value of y when x = -3?

Find the absolute maximum and minimum values of f(x, y) = y2 - y - x - 5 on the square0 ≤\le≤ x ≤\le≤ 1, 0 ≤\le≤ y ≤\le≤ 1.

Find the maximum and minimum values of f(x, y) = (x - y) .

Find the envelope of the family of straight lines y - 3 x + 2 = 0.

Find the values of constant real numbers a and b to minimize dx.

Find the absolute maximum and minimum values of f(x, y) = 2 - x2 - 4y on the diskx2 + y2 ≤\le≤ 9.

Find the absolute maximum and minimum values of f(x, y, z) = xyz(1 - x2 - y2 - z2) on the tetrahedron bounded by x = 0, y = 0, z = 0, and x + y + z = 2.

Preliminaries

Limits and Continuity

Differentiation

Transcendental Functions

More Applications of Differentiation

Integration

Techniques of Integration

Applications of Integration

Conics, Parametric Curves, and Polar Curves

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Find the absolute maximum and minimum values of f(x, y) = y² - y - x - 5 on the square0 $\le$ x $\le$ 1, 0 $\le$ y $\le$ 1.

Find the absolute maximum and minimum values of f(x, y) = 2 - x² - 4y on the diskx² + y² $\le$ 9.

Find the absolute maximum and minimum values of f(x, y, z) = xyz(1 - x² - y² - z²) on the tetrahedron bounded by x = 0, y = 0, z = 0, and x + y + z = 2.